The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making

Authors: Shouzhen Zeng

Abstract:

We present a new intuitionistic fuzzy aggregation operator called the intuitionistic fuzzy ordered weighted averaging-weighted average (IFOWAWA) operator. The main advantage of the IFOWAWA operator is that it unifies the OWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to deal with an uncertain environment that can be assessed with intuitionistic fuzzy numbers. We study some of its main properties and we see that it has a lot of particular cases such as the intuitionistic fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA (IFOWA) operator. Finally, we study the applicability of the new approach on a financial decision making problem concerning the selection of financial strategies.

Keywords: Intuitionistic fuzzy numbers, Weighted average, OWA operator, Financial decision making

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328546

References:

[1] G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A guide for practitioners, Springer-Verlag, Berlin, 2007.
[2] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.
[3] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating Information", International Journal of Intelligent Systems, vol. 18, pp. 953-969, 2003.
[4] R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making", IEEE Transactions on Systems, Man and Cybernetics, vol. 18, pp. 183-190, 1988.
[5] N. Karayiannis, "Soft Learning Vector Quantization and Clustering Algorithms Based on Ordered Weighted Aggregation Operators", IEEE Transaction Neural Networks, vol. 11, 1093-1105, 2000.
[6] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Optimization and Decision Making, vol. 3, pp.93-107, 2004.
[7] G. Beliakov, "Learning Weights in the Generalized OWA Operators", Fuzzy Optimization and Decision Making, vol. 4, pp. 119-130, 2005.
[8] P. Liu. A weighted aggregation operators multi-attribute group decision making method based on interval-valued trapezoidal fuzzy numbers. Expert Systems with Applications, vol. 38, pp. 1053-1060, 2011.
[9] B.S. Ahn, and H. Park, "Least-squared ordered weighted averaging operator weights", International Journal of Intelligent Systems, vol. 23, pp. 33-49, 2008.
[10] X.W. Liu, "The solution equivalence of minimax disparity and minimum variance problems for OWA operators", International Journal of Approximate Reasoning, vol. 45, pp. 68-81, 2007.
[11] J.M. Merig├│, "The induced generalized hybrid averaging operator and its application in financial decision making", International Journal of Human and Social Sciences, vol. 4, pp. 1014-1019, 2009
[12] J.M. Merig├│, "Fuzzy decision making with immediate probabilities", Computers & Industrial Engineering, vol. 58, pp. 651-657, 2010.
[13] J.M. Merig├│, "A unified model between the weighted average and the induced OWA operator", Expert Systems with Applications, vol.38, pp. 11560-11572, 2011.
[14] J.M. Merig├│, "The probabilistic weighted average and its application in multiperson decision making", International Journal of Intelligent Systems, vol. 27, pp. 457-476, 2012
[15] J.M. Merig├│, and M. Casanovas, "Decision making with distance measures and induced aggregation operators", Computers & Industrial Engineering, vol. 60, pp. 66-76, 2011.
[16] J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA operator", Information Sciences, vol. 179, pp. 729-741, 2009.
[17] J.M. Merig├│, and A.M. Gil-Lafuente, "New decision-making techniques and their application in the selection of financial products", Information Sciences, vol. 180, pp. 2085-2094, 2010.
[18] J.M. Merig├│, and A.M. Gil-Lafuente, "OWA operators in human resource management", Economic Computation and Economic Cybernetics Studies and Research, vol. 45, pp. 153-168, 2011.
[19] G.W. Wei, "FIOWHM operator and its application to group decision making", Expert Systems with Applications, vol. 38, pp. 2984-2989, 2011.
[20] Y.J. Xu, and H.M. Wang, "Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment", Applied Soft Computing, vol. 11, pp. 3988-3997, 2011.
[21] Z.S. Xu, and M.M. Xia, "Induced generalized intuitionistic fuzzy operators", Knowledge-Based Systems, vol. 24, pp. 197-209, 2011.
[22] L.G. Zhou, and H.Y. Chen, "Continuous generalized OWA operator and its application to decision making", Fuzzy Sets and Systems, vol. 16, pp. 18-34, 2011.
[23] V. Torra, "The weighted OWA operator", International Journal of Intelligent Systems, vol. 12, pp. 153-166, 1997.
[24] K.T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.
[25] G.W. Wei, "Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting", Knowledge-Based Systems, vol.21, pp. 833-836, 2008.
[26] G.W. Wei, "Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making", Applied Soft Computing, vol. 10, pp. 423-431, 2010.
[27] Z.S. Xu, "Intuitionistic fuzzy aggregation operators", IEEE Transactions on Fuzzy Systems, vol. 15, pp. 1179-1187, 2007.
[28] J. Ye, "Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment", European Journal of Operational Research, vol. 205, pp. 202-204, 2010.
[29] Z.S. Xu, and R.R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets", International Journal of General Systems, vol. 35,pp. 417-433, 2006.
[30] Y.J. Xu, and H.M. Wang, "The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making", Applied Soft Computing, vol. 2012, pp. 1168-1179, 2012.
[31] S.Z. Zeng, and W.H. Su, "Intuitionistic fuzzy ordered weighted distance operator" , Knowledge-Based Systems, vol. 24, pp. 1224-1232, 2011.
[32] S.Z. Zeng, "Some intuitionistic fuzzy weighted distance measures and their application to group decision making", Group Decision and Negotiation, in press. DOI:10.1007/s10726-011-9262-6.